Inverted Grounded-Cathode Amplifier
My last blog entry provoked some head scratching, as I deduced from the e-mail asking for clarification on the following circuit:

It wasn't just the two batteries that confused, but the cathode-follower-looking appearance of the topology. The e-mails asked, "How can there be any gain at all, when this circuit is clearly a unity-gain cathode follower?"

(Back in the year 2000, I wrote an article entitled Circlotron Relativity which is—beyond it electronic explication—an exercise in mental flexibility. I recommend that you give this old article a reading to help limber you up for what will follow.)

Appearances often deceive. In other words, looking like a cathode follower is not enough to make a circuit be a cathode follower. In the political domain, the question to ask is, Who gains? In an analog electronic circuit, the question to ask is, Where's the input signal's reference located? This referance point is usually the ground, but not always; just as a car's engine is usually located in the front, but not always. Where this referance point is fixed makes a triode function as a grounded-cathode amplifier or a cathode follower in the two circuits below.

The above circuit is an amplifier, not a unity-gain buffer. The input transformer allows the input signal’s reference to be situated at the amplifier’s output, not ground. Because this reference rides with the output signal, the output swings in phase with the input signal, with gain, with a relatively-high output impedance, and with a fairly-poor PSRR figure. How does it work? As the grid sees (relative to its cathode) a more positive input signal, the triode increases in its conduction, imposing a greater voltage drop across the 5k load resistor, which in turn forces the output to swing positively. Conversely, when the grid sees a more negative input signal, the triode decreases in its conduction, developing a smaller voltage drop across the 5k load resistor, forcing the output to swing negatively. Thus, there is no phase inversion. As long as the load resistor (and the external load impedance in parallel with this resistor) is larger than (rp + [mu + 1]Rk)/(mu – 1), the gain will exceed unity. In fact the formula for gain is the same as the grounded-cathode amplifier:

Gain = muR/(R + rp + [mu + 1]Rk),

where R is the total load resistance. And the formula for the output impedance is the same as the grounded-cathode amplifier:

Zo = R || (rp + [mu + 1]Rk).

Aside from the lack of phase inversion, the main difference between the inverted amplifier and the grounded-cathode amplifier is the former's PSRR formula, which is—befitting an inverted topology—the inversion of the grounded-cathode amplifier’s:

PSRR = R/(R + rp + [mu + 1]Rk).

In the schematic above, the load resistor’s low resistance makes for a better PSRR figure, just the opposite of a grounded-cathode amplifier with the same valued parts. Now, think extremely: imagine a constant-current source in place of the 5k load resistor. What would be the PSRR figure for the inverted amplifier? With a grounded-cathode amplifier, a constant-current source plate load equals an infinite reduction in power-supply noise to the output. But what happens in an inverted amplifier? The answer is that nearly all the power-supply noise bleeds into the output. Now, before anyone jumps to some silly conclusion that the inverted circuit is worthless, let me remind you that in the circuit shown above, the PSRR is twice as good as the comparable grounded-cathode amplifier with the same resistor values, because of the low-ohmage load resistor. Furthermore, never completely discount any circuit, as you never know when you might need its set of attributes and what may seem a liability could prove an asset in a different circuit configuration.

I love getting preachy, which is why I hate doing it. Nonetheless, I have to stress the point that being good at analog electronics is like being good any art form, be it writing, painting, composing, sculpting: you must know as many techniques as you can, but be discriminating. Use only those techniques that work best with each creation. In short, know all you can but be shrewd in applying what you know.

Being a tube guru stands in stark contrast, as the guru knows as few techniques, perspectives, philosophies, and alternatives as he can get away with. He sees it the same way all religious fanatics see it: Why should he waste his time on what is not the one and only true course? The tube guru wants to lead you down his secret path, not show you a Google Earth map of where you are and where you want to go. I wish I had a beer for every time I have been told that the only thing worth listening to was...a Circlotron or cascode or SRPP or balanced or single-ended or push-pull or feedback-free or heavy-feedback circuits, or only 9-pin tubes, octal tubes, RCA tubes, anything-but RCA tubes, DHT amplifiers, Teflon capacitors, PIO capacitors, wet-slug tantalum capacitors, polypropylene-foil capacitors, beeswax capacitors…

Back to circuits, both formulas being the same as the grounded-cathode amplifier's makes sense, as the triode has no idea what circuit it is in; it only knows voltage relationships: the voltage differential between its cathode and its plate and between its cathode and its grid. These voltage relationships dictate its current conduction, blindly, unvaryingly.

Now in the following circuit, let us move the input signal’s reference point to ground. A 50V battery is used to bias the cathode follower’s grid and the battery, being an ideal battery, offers no AC impedance, so the transformer’s secondary is effectively grounded at one end.

Note how all the DC voltage relationships remain constant, yet this circuit is now a cathode follower, with no gain and low output impedance. The last attribute is worth looking into. Imagine forcing the triode’s cathode more positive by an externally applied pulse. What would happen? The grid would effectively become more negative relative to the cathode and the triode’s conduction would drop, thereby bucking that positive-going perturbation at its cathode, as the 5k load resistor will tug negatively at the output. Conversely, a negative-going perturbation would effectively make the grid more positive relative to the cathode and the triode’s conduction would increase, causing an upward tug at the output.

Now apply the same positive and negative perturbations on the inverted amplifier’s output. In both cases the grid would see only a small fraction of the pulse’s magnitude, as input signal’s reference is tied to the amplifier’s output. Because the grid sees almost the same magnitude of pulse as the cathode sees, the triode only responds with a fraction of current conduction swing that the cathode-follower circuit realizes, greatly increasing the output impedance.

Before leaving the inverted-grounded-cathode-amplifier topology, I should point out how this topology could work with a negative power supply.

It is interesting, but what good is it? Well, how about this scenario: a low-mu triode, such as the 845 or 6C33 or 6AS7 has its cathode grounded and its plate loaded by an output transformer; its grid directly coupled to a circuit like the one above, but without the coupling capacitor. Now stop and think about why this amplifier would prove much safer than the following.

The answer is that if the driver tube were removed, the output tube would not melt down. The grid falls to -200V in the circuit below, but climbs to 0V in the circuit above. For the same reason, startup is much safer with the inverted amplifier topology; remember, a tube cannot conduct until it’s hot.

Transformer-Coupled Aikido Line-Stage Amplifier
Now that we are mentally limber and the inverted-grounded-cathode-amplifier topology no longer seems strange, let's move on to some interesting circuits. At the top of this blog entry, we see the Aikido phono pre-preamp circuit, but there is no reason that we cannot use this topology elsewhere, in a line stage amplifier for example. The following circuit uses an input transformer to DC isolate the signal source completely from the line stage amplifier; note the absence of a ground connection on the transformer’s primary. Once the input signal has been reflected across the input transformer, the input triode amplifies, while the second tube buffers the output signal. Power-supply noise is dropped from the output and the output coupling capacitor provides a safety net.

Note the two power supply shunting capacitors that do not terminate into ground. This arrangement ensures that the power-supply noise on the positive and negative rails are related, differing only in phase. Assuming that dual-triode tubes, such as the 6DJ8, 6H30, 6SN7, 12AU7, 12BH7, and 5687, are used and that the triodes are distributed vertically, not horizontally, a single heater power supply can be used, but it must be referenced to -75V, in this example.

Now I know that many readers are wondering why an output coupling capacitor is used, as the output seems to be DC-offset free. The answer is that while the DC offset is likely to be close to 0V, it will still be too far off to be safe, particularly with DC-coupled solid-state power amplifiers. Although the simple output-coupling-capacitor is both easy and safe, some will be tempted by the DC servo loop alternative shown below.

To be honest, I don’t see much of an advantage to this circuit over the previous one, as we must still endure a coupling capacitor in the signal path, albeit a much smaller-valued one. Furthermore, a +/-15V power supply will be needed. On the other hand, if you expect to drive a wide range of impedances, say from 10k to 1M, the servo-loop version can look more appealing. (The diode is my signature touch to the basic DC servo loop; it is a safety feature that works much better with a simple load resistor, not the tube-based active load. Still, it would help in half the failure situations, wherein the output swings excessively negative.)

The following circuit does away with all coupling capacitors. The OpAmp still monitors the DC offset at the output and its output swings in a contrary polarity, but it does not directly apply a corrective grid bias voltage; instead, it tugs the input stage’s output up and down via the 30k resistor.

The two zeners on the output are there as a small safety feature, as they will limit the maximum output swing to roughly +/-6V. This may not seem like much, but it is much better than the potentially ruinous +/-150V.

Aikido-Unicorn Phono Preamp

Click on schematic to see closeup

Just to help further establish my non-guru status, I present the above original circuit. Non-guru? If I were a tube guru (or a better businessman) I would never distract you with more phono preamp circuits; instead, I would claim that the Aikido PH-1 phono stage was perfect and that all other phono stages are laughingly inferior. As for the name, Aikido-Unicorn, back in 2002, I wrote an essay titled, RIAA Preamps Part 2, wherein on page 10 the Unicorn topology made its first showing:

Fresh Topology
If fewer caps are better, is it possible to build a multi-tube passive phono preamp with only one coupling capacitor? In the circuit below we see a constant-current-draw amplifier feeding a passive equalization network, which then feeds a common-cathode amplifier, amazingly DC coupled all the way to the output coupling capacitor. The 100-volt DC bias voltage on the network's output allows us to use a rather large valued common-cathode resistor (5200-ohms) without having to use a negative power supply.

The enemy of all preamplifiers is noise. Some noises are difficult if not impossible to counter, such as tube microphonics. One source of noise, however, can be reduced through an understanding and the careful applications of noise mulling techniques. The elaborate circuitry at the common-cathode's second triode's grid (the 1-meg resistor and the two capacitors in series) is there to allow canceling of the power supply’s noise from its output by introducing a small amount of power supply noise at this grid by effectively voltage dividing the power supply’ noise. Thus this portion of the power supply noise can be amplified and phase inverted at the output, where it will cancel with the power supply noise at the plate resistor. A single coupling capacitor is in itself a worthy enough goal, but by adding noise cancellation, we arrive at a truly desirable phono stage.

Notice how the 3.3k resistor in the power supply serves double duty by filtering the B+ voltage for the first stage and achieving a matched plate voltage for the second stage’s triodes. A safe bet would be a floating heater power supply that was referenced to about 70 volts to prevent exceeding the triode’s cathode-to- heater voltage limits.

(Of course, my brief outlining of this circuit is not the correct tube-guru procedure to promoting a new design. The generally accepted guru approach would be to write a long article for a mainstream—or is minor-stream closer to the truth?—audio magazine, such as the late Sound Practices. The article would then go on to slam all other tube phono preamp designs and go on to explain how the preamp sounds far better than a friend’s supremely-expensive-tube-name-brand preamp. The article would explain how the preamp must be made with both the carbon resistors and the capacitors culled from a 1961 RCA BW television; in fact, the preamp would be named the RCA Uni-Cap preamp, or better still, the RCA-Unicorn preamp. This circuit would then live and propagate, becoming user-group and chat-room fodder; finally, someone would use a different tube and claim to have invented a whole new topology or it might mutate into a simpler circuit, as few would understand how the noise cancellation works and what is not understood is not needed; right? Oh, what a tube-audio cynic I have become.)

// JRB

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Hi John,

I received the Aikido PCB today - thank you for the first rate shipping speed.

Wanted to let you know that this is simply the best PCB I have had in my hands, bar none. The quality is fabulous, and your documentation is superb. I know you do this because you love audio, but I think your price of $39 is a bit of a giveaway! I'm sure you could charge double and still have happy customers.

Looking forward to building the Aikido, will send some comments when I'm done!

Thank you, regards, Gary.

Mr Broskie,

I bought an Aikido stereo linestage kit from you some days ago, and I received it just this Monday. I have a few things to say about it.. Firstly, I'm extremely impressed at the quality of what I've been sent. In fact, this is the highest quality kit I've seen anywhere, of anything. I have no idea how you managed to fit all this stuff in under what I paid for it. Second, your shipping was lightning-quick. Just more satisfaction in the bag, there. I wish everyone did business like you.

TCJ Push-Pull Calculator has but a single purpose: to evaluate tube-based output stages by simulating eight topologies’ (five OTL and three transformer-coupled) actual performance with a specified tube, power supply and bias voltage, and load impedance. The accuracy of the simulation depends on the accuracy of the tube models used and the tube math model is the same True Curves™ model used in GlassWare's SE Amp CAD and Live Curves programs, which is far more accurate than the usual SPICE tube model.